Question 1

A hospital collects the following waiting times (in minutes) for five patients: 12, 15, 9, 20, and 14. What is the mean waiting time?

$$\bar{x} = \dfrac{\sum x}{n}$$

Accepted Answer

$$\bar{x} = 14$$ minutes

Question 2

Which measure of center is most resistant to outliers in a data set?

Accepted Answer

Median

Question 3

Given the data set: 8, 12, 15, 20, 25, what is the midrange?

$$	ext{Midrange} = \dfrac{	ext{maximum value} + 	ext{minimum value}}{2}$$

Accepted Answer

$$	ext{Midrange} = 16.5$$

Question 4

A researcher finds the following cholesterol levels (mg/dL) in a sample: 180, 190, 200, 210, 220. What is the median cholesterol level?

Accepted Answer

200 mg/dL

Question 5

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is a resistant measure of variation.

Question 6

A sample of five exam scores is: 70, 75, 80, 85, 90. What is the range?

$$	ext{Range} = 	ext{maximum value} - 	ext{minimum value}$$

Accepted Answer

$$	ext{Range} = 20$$

Question 7

The IQ scores in a population are normally distributed with a mean of 100 and a standard deviation of 15. According to the empirical rule, what percentage of IQ scores are between 85 and 115?

(Empirical rule: About 68% of values fall within 1 standard deviation of the mean.)

Accepted Answer

About 68%

Question 8

A platelet count of 75 (in thousands/μL) is observed in a population with mean $$\mu = 250$$ and standard deviation $$\sigma = 68.4. $$Calculate the z score for this platelet count.

$$z = \dfrac{x - \mu}{\sigma}$$

Accepted Answer

$$z = -2.56$$

Question 9

Which of the following best describes the coefficient of variation (CV) for a sample?

$$CV = \dfrac{s}{\bar{x}} 	imes 100$$

Accepted Answer

It measures the standard deviation relative to the mean, expressed as a percent.

Question 10

A data set has a minimum value of 2, Q1 = 5, median = 8, Q3 = 12, and maximum value of 20. What is the interquartile range (IQR)?

$$IQR = Q_3$ - Q_1$

Accepted Answer

$$IQR = 7$$

Question 11

Which of the following scenarios would make the mean an inappropriate measure of center?

Accepted Answer

A data set of zip codes for different cities.

Question 12

Given the following five-number summary for a data set: 10, 20, 30, 40, 100, which value is most likely an outlier based on the 1.5 × IQR rule?

Accepted Answer

100

Question 13

A boxplot is constructed for a data set. If the box is much closer to the lower whisker than the upper whisker, what does this suggest about the distribution?

Accepted Answer

The distribution is skewed right.

Question 14

A sample of data has a mean of 50 and a standard deviation of 5. According to the range rule of thumb, what is the approximate range of the data?

$$	ext{Range} \approx 4s$$

Accepted Answer

20

Question 15

Which of the following is true about the variance of a data set?

Accepted Answer

It is the square of the standard deviation.

Question 16

A data set has the following values: 2, 4, 4, 4, 5, 7, 9. What is the mode?

Accepted Answer

4

Question 17

If a value has a z score of 2.5, what can you conclude about this value?

Accepted Answer

It is significantly high.

Question 18

Which of the following best describes a bimodal data set?

Accepted Answer

It has two values that occur with the same greatest frequency.

Question 19

A sample of 10 patients has a mean blood pressure of 120 mmHg and a sample standard deviation of 15 mmHg. What is the sample variance?

$$s^2 = s$$ 	imes s$$

Accepted Answer

$$225$$ mmHg$$^2$$

Question 20

Which of the following is NOT included in the five-number summary?

Accepted Answer

Mean

Chapter 3: Describing, Exploring, and Comparing Data – Biostatistics Study Notes

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